To the issue of being married... yes they can deport you and they will, if you do not go through OFII and get the carte de sejour. Being married does not allow you to stay in the country illegally. BUT it does make things easier.
I married before going back to the States to get my Visa. It made things easier, but I was still required to go back and get the Visa before applying for the carte de sejour.
As Claire stated, the folks at OFII are really nice. I went through the exact same process in Marsaille. It's a half day, but not unpleasant. The xray and all are free. The money you pay is a "tax" for getting the carte de sejour. Then I had to go to a required class for one day to learn about the Republic of France. Some people also have to go through employment and language classes. I was exempted from these by the nice lady at OFII.
Suzy, the one year visa is meant for persons only staying in France for 1 year. If your son's girlfriend is planning to stay, she NEEDS that carte de sejour. I'm only telling you this so she doesn't go through this again next year. They may deny her a visa if she keeps relying on it. As soon as she gets back, have her go to OFII. Believe me, it's not bad, and much better than the worry of what will happen next year.
What IS difficult, is the second year when you renew your carte de sejour. I'm in that process now, and OFII was nothing compared to what I've been through with the sous prefecture. Back to the issue of being married.... they require you PROVE you are really married and not just having an arrangement so you can get into the country. I had to present paperwork showing both of our names, such as electric and phone bill and bank account. And then they sent the gendarmes to my house just last week. They were nice, but they stayed for two hours asking questions and looking around the house (even in my closets) to see if we were indeed co-habitating.
So, I've been told that the first year OFII is pretty lax and gives you the carte de sejour, but the renewal is more difficult. This has been my experience. But it's the only way to legally stay in the country. And if your son and his girlfriend are not married, she's going to have to produce paperwork showing that she has a permanent address (her name on the paperwork) and that she has income and insurance. The basic requirements, provided in the law, are that immigrants can show they have a place to live and they have "sufficient" income.
Here's another piece of advice that I missed. If she's planning to live here, make sure she gets a paper while in the States from the Consulate for moving personal items if she plans to ship anything over. You have to have this paper to avoid taxes and you have to ship within the first year. Same with French driving permit. Do it within the first year. I didn't due to problems with my last name on passport and driver's license (divorced in States and re-married here) and I'm having difficulties with both now.
Best wishes to her.